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plotnumerical-methodsmaximapiecewise

How to draw graph of Gauss function?

Gauss function has an infinite number of jump discontinuities at x = 1/n, for positive integers.

I want to draw diagram of Gauss function.

Using Maxima cas I can draw it with simple command : 

  f(x):= 1/x - floor(1/x);  plot2d(f(x),[x,0,1]);

enter image description here

but the result is not good ( near x=0 it should be like here)

Also Maxima claims:

plot2d: expression evaluates to non-numeric value somewhere in plotting range.

I can define picewise function ( jump discontinuities at x = 1/n, for positive integers )

so I tried : 

define( g(x), for i:2 thru 20 step 1 do if (x=i) then x else (1/x) - floor(1/x));

but it don't works.

I can also use chebyshew polynomials to aproximate function ( like in : A Graduate Introduction to Numerical Methods From the Viewpoint of Backward Error Analysis by Corless, Robert, Fillion, Nicolas)

How to do it properly ?

Solution

  • I have made a list of segments with ending points. The result is : enter image description here

    and full code is here

    Edit: smaller size with shorter lists in case of almost straight lines,

    if (n>20) then iMax:10 else iMax : 250,

    in the GivePart function